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Evaluation of the Recursive Projection Method for Efficient Unsteady Turbulent CFD Simulations
KTH, Superseded Departments, Aeronautical and Vehicle Engineering.
KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
2004 (English)In: 24th INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES, 2004, 1-13 p.Conference paper, Published paper (Refereed)
Abstract [en]

The Recursive Projection Method (RPM) hasbeen implemented into an unstructured CFD code to improve the efficiency of dual time steppingfor unsteady turbulent CFD simulations.RPM is a combined implicit-explicit method that enhances convergence. It can easily be implementedinto existing codes and the solver’s existing acceleration techniques can be used withoutchange. The method has been evaluated by computing the periodic self-induced shock oscillations over an 18% thick biconvex airfoil at0◦ angle of attack, a Mach number of 0.76 anda Reynolds number of 11 million. On average,RPM accelerated the convergence of the innerloop of dual time stepping to a predefined convergencecriterion by a factor of about 2.5.

Place, publisher, year, edition, pages
2004. 1-13 p.
Keyword [en]
Recursive Projection Method, CFD, dual time stepping, convergence, unsteady flow, buffet
National Category
Computer Engineering Vehicle Engineering
Identifiers
URN: urn:nbn:se:kth:diva-4907OAI: oai:DiVA.org:kth-4907DiVA: diva2:6779
Conference
24th INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES
Note
QC 20101015Available from: 2005-02-02 Created: 2005-02-02 Last updated: 2010-10-19Bibliographically approved
In thesis
1. Aspects of the recursive projection method applied to flow calculations
Open this publication in new window or tab >>Aspects of the recursive projection method applied to flow calculations
2005 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

In this thesis, we have investigated the Recursive Projection Method, RPM, as an accelerator for computations of both steady and unsteady flows, and as a stabilizer in a bifurcation analysis.

The criterion of basis extraction is discussed. It can be interpreted as a tolerance for the accuracy of the eigenspace spanned by the identified basis, alternatively it can be viewed as a criterion when the approximative Krylov sequence becomes numerically rank deficient.

Steady state calculations were performed on two different turbulent test-cases; a 2D supersonic nozzle flow with the Spalart-Allmaras 1-equation model and a 2D sub-sonic airfoil simulation using the κ - ε model. RPM accelerated the test-cases with a factor between 2 and 5.

In multi-scale problems, it is often of interest to model the macro-scale behavior, still retaining the essential features of the full systems. The ``coarse time stepper'' is a heuristic approach for circumventing the analytical derivation of models. The system studied here is a linear lattice of non-linear reaction sites coupled by diffusion. After reformulation of the time-evolution equation as a fixed-point scheme, RPM coupled with arc-length continuation is used to calculate the bifurcation diagrams of the effective (but analytically unavailable) equation.

Within the frame-work of dual time-stepping, a common approach in unsteady CFD-simulation, RPM is used to accelerate the convergence. Two test-cases were investigated; the von Karman vortex-street behind a cylinder at Re=100, and the periodic shock oscillation of a symmetric airfoil at M ∞ = 0.76 with a Reynolds number Re=11 x 106.

It was believed that once a basis had been identified, it could be retained for several steps. The simulations usually showed that the basis could only be retained for one step.

The need for updating the basis motivates the use of Krylov methods. The most common method is the (Block-) Arnoldi algorithm. As the iteration proceeds, Krylov methods become increasingly expensive and restart is required. Two different restart algorithm were tested. The first is that of Lehoucq and Maschhoff, which uses a shifted QR iteration, the second is a block extension of the single-vector Arnoldi method due to Stewart. A flexible hybrid algorithm is derived combining the best features of the two.

Place, publisher, year, edition, pages
Stockholm: KTH, 2005. ix, 26 p.
Series
Trita-NA, ISSN 0348-2952 ; 0444
Keyword
Datorteknik, applied mechanics, computer science, aerospace, Datorteknik
National Category
Computer Engineering
Identifiers
urn:nbn:se:kth:diva-101 (URN)91-7283-940-6 (ISBN)
Public defence
2005-01-20, Sal L1, Drottning Kristinas väg 30, Stockholm, 10:15
Opponent
Supervisors
Note

QC 20101015

Available from: 2005-02-02 Created: 2005-02-02 Last updated: 2012-09-21Bibliographically approved
2. Realistic simulations of delta wing aerodynamics using novel CFD methods
Open this publication in new window or tab >>Realistic simulations of delta wing aerodynamics using novel CFD methods
2005 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

The overall goal of the research presented in this thesis is to extend the physical understanding of the unsteady external aerodynamics associated with highly maneuverable delta-wing aircraft by using and developing novel, more efficient computational fluid dynamics (CFD) tools. More specific, the main purpose is to simulate and better understand the basic fluid phenomena, such as vortex breakdown, that limit the performance of delta-wing aircraft. The problem is approached by going from the most simple aircraft configuration - a pure delta wing - to more complex configurations. As the flow computations of delta wings at high angle of attack have a variety of unusual aspects that make accurate predictions challenging, best practices for the CFD codes used are developed and documented so as to raise their technology readiness level when applied to this class of flows.

Initially, emphasis is put on subsonic steady-state CFD simulations of stand-alone delta wings to keep the phenomenon of vortex breakdown as clean as possible. For half-span models it is established that the essential characteristics of vortex breakdown are captured by a structured CFD code. The influence of viscosity on vortex breakdown is studied and numerical results for the aerodynamic coefficients, the surface pressure distribution and breakdown locations are compared to experimental data where possible.

In a second step, structured grid generation issues, numerical aspects of the simulation of this nonlinear type of flow and the interaction of a forebody with a delta wing are explored.

Then, on an increasing level of complexity, time-accurate numerical studies are performed to resolve the unsteady flow field over half and full-span, stationary delta wings at high angle of attack. Both Euler and Detached Eddy Simulations (DES) are performed to predict the streamwise oscillations of the vortex breakdown location about some mean position, asymmetry in the breakdown location due to the interaction between the left and right vortices, as well as the rotation of the spiral structure downstream of breakdown in a time-accurate manner. The computed flow-field solutions are visualized and analyzed in a virtual-reality environment.

Ultimately, steady-state and time-dependent simulations of a full-scale fighter-type aircraft configuration in steady flight are performed using the advanced turbulence models and the detached-eddy simulation capability of an edge-based, unstructured flow solver. The computed results are compared to flight-test data.

The thesis also addresses algorithmic efficiency and presents a novel implicit-explicit algorithm, the Recursive Projection Method (RPM), for computations of both steady and unsteady flows. It is demonstrated that RPM can accelerate such computations by up to 2.5 times.

Place, publisher, year, edition, pages
Stockholm: KTH, 2005. ix, 68 p.
Series
Trita-AVE, ISSN 1651-7660 ; 2005:01
Keyword
Space and plasma physics, CFD, aerodynamics, flow physics, steady, unsteady, delta wing, vortical flow, Rymd- och plasmafysik
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-125 (URN)91-7283-938-4 (ISBN)
Public defence
2005-02-15, Kollegiesalen, Valhallavägen 79, Stockholm, 10:15
Opponent
Supervisors
Note
QC 20101019Available from: 2005-02-11 Created: 2005-02-11 Last updated: 2010-10-19Bibliographically approved

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